1. Sine Rule for Angles Ex1 P Q R 18 20 sin42° sinQ° =
sin42° sinQ° =
42°
20cm
18 X sinQ° = 20 X sin42°
sinQ° = 20 X sin42°  18
18cm
sinQ° = ….
(min 3 dps)
Find angles Q and R.
Q° = sin
= 48°  
p q r
sinP sinQ sinR
= =
R° = 180° – 42° - 48°  ? ?
= 90°

2. Ex2 F G H 30 17 sin72° sinH° = 30 X sinH° = 17 X sin72°
sin72° sinH° =
72°
17cm
30 X sinH° = 17 X sin72°
sinH° = 17 X sin72°  30
30cm
sinH° = ….
(min 3 dps)
Find angles G and H.
H° = sin
= 32.6°  
f g h
sinF sinG sinH
= =
R° = 180° – 72° °  ? ?
= 75.4°

3. Ex3
In a lop-sided roof the longer side is 3.2m and slopes at an angle of 32° to the horizontal. The shorter side is 1.7m and makes an angle of c° with the horizontal. Find c°.
3.2m
1.7m c°
32°
sinc° sin32° = X Y Z
3.2m
1.7m
32° c°
1.7 x sinc° = x sin32°
sinc° = x sin32°  1.7 
sinc° = 
x y z
sinX sinY sinZ
= =
c° = sin  ?
= 86°

4. If A + B = 180 then sinA° = sinB°
Obtuse Angles
A B A+B sinA° sinB°
180
0.342
0.342
180
0.574
0.574
180
0.940
0.940
180
0.682
0.682
CONCLUSION
If A + B = 180 then sinA° = sinB°
Ex4
sinx° = 0.643
so x = sin
= 40°
or 140°

5. Ex5
In ABC a = 4, b = 7 & angle A = 30°. Find two possible sizes for angle B. A B C
7cm
4cm
30° 
a b c
sinA sinB sinC
= =